We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of m^2=n^2+nl+l^2.

# Publications

## Pages

Let c_n = c_n(d) denote the number of self-avoiding walks of length n starting at the origin in the Euclidean nearest-neighbour lattice \mathbb{Z}^d. Let \mu = \lim_n c_n^{1/n} denote the...

The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a...

Given a real function f on an interval [a,b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f,f′ and f...

We prove a local law for the adjacency matrix of the Erd\H{o}s-R\'enyi graph G(N,p) in the supercritical regime pN \geq C\log N where G(N,p) has with high probability no isolated vertices. In...

The celebrated Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory describes the universal correlations of eigenvalues on the microscopic scale, i.e....

We study complex CFTs describing fixed points of the two-dimensional Q-state Potts model with Q>4. Their existence is closely related to the weak first-order phase transition and walking RG...

During single clock inflation, hidden fields (i.e. fields coupled to the inflaton only gravitationally) in their adiabatic vacua can ordinarily only affect observables through virtual effects....

Given a graph G and a bijection f : E(G)\rightarrow \{1, 2, \ldots,e(G)\}, we say that a trail/path in G is f-\emph{increasing} if the labels of consecutive edges of this trail/path form an...

For a compact Poisson-Lie group K, the homogeneous space K/T carries a family of symplectic forms\omega_\xi^s, where \xi \in \mathfrak{t}^*_+ is in the positive Weyl chamber and s \in \mathbb{R...

We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze the limit...

We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the...